@Article{Graef2020,
author = "Graef, John R. and Grace, Said R. and Tunç, Ercan",
title = "On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "2",
pages = "227--239",
doi = "https://doi.org/10.7494/OpMath.2020.40.2.227",
url = "https://doi.org/10.7494/OpMath.2020.40.2.227",
abstract = "This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form \[^{C}D_{c}^{\alpha}y(t)+f(t,x(t))=e(t)+k(t)x^{\eta}(t)+h(t,x(t)),\] where \(t\geq c \geq 1\), \(\alpha \in (0,1)\), \(\eta \geq 1\) is the ratio of positive odd integers, and \(^{C}D_{c}^{\alpha}y\) denotes the Caputo fractional derivative of \(y\) of order \(\alpha\). The cases \[y(t)=(a(t)(x^{\prime}(t))^{\eta})^{\prime} \quad \text{and} \quad y(t)=a(t)(x^{\prime}(t))^{\eta}\] are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.",
keywords = "integro-differential equations, fractional differential equations, nonoscillatory solutions, boundedness, Caputo derivative",
issn = "1232-9274"
}